%%%% prbla_05.ldf
%%%% Created by Laurence D. Finston (LDF) Thu Nov 17 22:28:24 CET 2005
%% * (1) Copyright and License.
%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing.
%%%% Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 The Free Software Foundation
%%%% GNU 3DLDF is free software; you can redistribute it and/or modify
%%%% it under the terms of the GNU General Public License as published by
%%%% the Free Software Foundation; either version 3 of the License, or
%%%% (at your option) any later version.
%%%% GNU 3DLDF is distributed in the hope that it will be useful,
%%%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%%%% GNU General Public License for more details.
%%%% You should have received a copy of the GNU General Public License
%%%% along with GNU 3DLDF; if not, write to the Free Software
%%%% Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
%%%% GNU 3DLDF is a GNU package.
%%%% It is part of the GNU Project of the
%%%% Free Software Foundation
%%%% and is published under the GNU General Public License.
%%%% See the website http://www.gnu.org
%%%% for more information.
%%%% GNU 3DLDF is available for downloading from
%%%% http://www.gnu.org/software/3dldf/LDF.html.
%%%% Please send bug reports to Laurence.Finston@gmx.de
%%%% The mailing list help-3dldf@gnu.org is available for people to
%%%% ask other users for help.
%%%% The mailing list info-3dldf@gnu.org is for the maintainer of
%%%% GNU 3DLDF to send announcements to users.
%%%% To subscribe to these mailing lists, send an
%%%% email with ``subscribe '' as the subject.
%%%% The author can be contacted at:
%%%% Laurence D. Finston
%%%% c/o The Free Software Foundation, Inc.
%%%% 51 Franklin St, Fifth Floor
%%%% Boston, MA 02110-1301
%%%% USA
%%%% Laurence.Finston@gmx.de
%% Run these commands:
%% 3dldf prbla_05.ldf
%% mpost prbla_05
%% tex prbla_05.txt
%% dvips -o prbla_05.ps prbla_05.dvi
%% gv prbla_05.ps &
%% *** (3) The intersection of a `parabola' and a linear `path'.
%% So far, I've only programmed the coplanar case.
%% LDF 2005.11.17.
verbatim_metapost "verbatimtex \magnification=\magstep5 \font\large=cmr12 etex";
focus f;
set f with_position (0, 10, -20) with_direction (0, 10, 100) with_distance 15;
pickup pencircle scaled (1mm, 1mm);
beginfig(1);
parabola p;
set p with_parameter 3 with_extent 7;
path q;
q := ((-5, 0, -5) -- (7, 0, 12)) shifted (5, 0, -2);
draw p with_color blue;
draw q;
pickup pencircle scaled (2mm, 2mm);
drawdot get_vertex p;
drawdot get_focus p;
label.lft("$v$", get_vertex p);
label.rt("$f$", get_focus p);
point_vector pv;
pv := p intersection_points q;
if size pv > 0:
drawdot pv0 with_color red;
label.lrt("$i_0$", pv0);
fi;
if size pv > 1:
drawdot pv1 with_color red;
label.lft("$i_1$", pv1 shifted -.333);
fi;
endfig with_projection parallel_x_z;
verbatim_metapost "end";
end;